Chaotic time series prediction based on attention-enhanced asynchronous optoelectronic reservoir computing

Despite the significant advantages of reservoir computing in enhancing performance, its application in predicting chaotic time series remains largely confined to short-term prediction. This limitation stems primarily from the inability of the ridge regression scheme to fully capture the sequential characteristics when deriving output weights, leading to an exponential increase in error accumulation over long-term prediction. By synergistically optimizing both hardware architecture and algorithm design, we introduce an innovative framework that integrates a multi-delay asynchronous optoelectronic reservoir with a self-attention mechanism. At the hardware level, system complexity is effectively reduced through a restructured topology of the optoelectronic reservoir and an asynchronous design of the time delay parameters driven by a single arbitrary waveform generator. At the algorithm level, the incorporation of a self-attention mechanism enables dynamic screening and weight allocation of the reservoir's high-dimensional states, overcoming the limitations of traditional methods in capturing global temporal dependencies. The results demonstrate that the proposed scheme achieves a significant reduction in the NMSE. In long-term predictions of up to 200 steps, the NMSE of our proposed scheme remains low and does not exceed 0.1. In contrast, the NMSE of the asynchronous RC scheme with ridge regression is about 2, that of the single RC scheme with ridge regression is about 5.5, that of the single RC scheme with self-attention mechanism is about 0.3.